MathAmigo

Integration

Secondary 4 Additional Math practice

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Integration practice questions

Secondary 4 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Find ∫(2x+1)3 dx\int (2x + 1)^{3} \, dx.
Show the worked solution
  • ∫(2x+1)3 dx=(2x+1)44×2+clinear chain rule\int (2x + 1)^{3} \, dx = \frac{(2x + 1)^{4}}{4 \times 2} + c \quad \scriptsize\textit{linear chain rule}
  • =18(2x+1)4+c= \frac{1}{8}(2x + 1)^{4} + c

Answer: 1/8(2x+1)4+c1/8(2x+1)^4+c

Example 2

Find ∫18sec⁡2(2x) dx\int 18\sec^2(2x) \, dx.
Show the worked solution
  • ∫18sec⁡2(2x) dx=18⋅12tan⁡(2x)+creverse of ddx[tan⁡(2x)]\int 18\sec^2(2x) \, dx = 18 \cdot \frac{1}{2}\tan(2x) + c \quad \scriptsize\textit{reverse of } \frac{d}{dx}[\tan(2x)]
  • =9tan⁡(2x)+c= 9\tan(2x) + c

Answer: 9tan(2x)+c9tan(2x)+c

Example 3

Find ∫6e2x+1 dx\int 6e^{2x + 1} \, dx.
Show the worked solution
  • ∫6e2x+1 dx=62e2x+1+clinear exponent rule\int 6e^{2x + 1} \, dx = \frac{6}{2} e^{2x + 1} + c \quad \scriptsize\textit{linear exponent rule}
  • =3e2x+1+c= 3e^{2x + 1} + c

Answer: 3e2x+1+c3e^{2x+1}+c

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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